# Euler's Theorems: Circuit, Path & Sum of Degrees

Instructions:

question 1 of 3

### If a graph has 15 edges, what must the degrees of the vertices add up to?

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### 1. The total number of degrees in a graph is 20. How many edges does it have?

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The quiz will give you limited details about a graph, such as the number of edges or vertices. You will need to use that information to infer other characteristics of the graph. Some other questions will present you with the image of a graph and require you to answer questions about its various properties.

## Quiz & Worksheet Goals

In order to answer these questions correctly, you will need to understand the following definitions:

• Edges and vertices
• Degrees in a graph
• Euler circuits
• Euler paths

## Skills Practiced

• Making connections - use understanding of the concept of circuits and graphs
• Problem solving - use acquired knowledge to solve circuit practice problems
• Defining key concepts - ensure that you can accurately define main phrases, such as edges and vertices
• Distinguishing differences - compare and contrast topics from the lesson, such as Euler paths and Euler circuits